Signal processing techniques such as filtering, detection, estimation and frequency domain analysis have long been applied to extract information from noisy sensor data. This paper describes the exploitation of these signal processing techniques to extract information from social networks, such as Twitter and Instagram. Specifically, we view social networks as noisy sensors that report events in the physical world. We then present a data processing stack for detection, localization, tracking, and veracity analysis of reported events using social network data. We show using a controlled experiment that the behavior of social sources as information relays varies dramatically depending on context. In benign contexts, there is general agreement on events, whereas in conflict scenarios, a significant amount of collective filtering is introduced by conflicted groups, creating a large data distortion. We describe signal processing techniques that mitigate such distortion, resulting in meaningful approximations of actual ground truth, given noisy reported observations. Finally, we briefly present an implementation of the aforementioned social network data processing stack in a sensor network analysis toolkit, called Apollo. Experiences with Apollo show that our techniques are successful at identifying and tracking credible events in the physical world.